Leigh A. Johnston1,2, Adel Foda2, Michael J. Farrell2,3, Gary F. Egan2,3
1School of Engineering & NICTA VRL, University of Melbourne, Melbourne, VIC, Australia; 2Howard Florey Institute, Florey Neuroscience Institutes, Melbourne, VIC, Australia; 3Centre for Neuroscience, University of Melbourne, Melbourne, VIC, Australia
Statistical analyses of fractional anisotropy images in diffusion MRI studies are traditionally approached using parametric tests, under Gaussianity assumptions, or nonparametric resampling techniques. We present an analytic form for the distribution of FA, both for Gaussian distributed tensor eigenvalues for which FA follows a transformed doubly noncentral beta distribution, and a generalisation to arbitrary eigenvalue distributions. These powerful result permits application of valid inference statistical tests to FA maps in all experimental conditions.